Amarjeet K. answered • 03/10/15

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When this curve rotates about x axis it will look like a trapeziod with radius of 1 unit (√(2-1))at one end and radius of 4 units (√(5-1)) at another end with height of 3 units (5-2=3_like a chopped off cone.

You can use calculus

volume of an infinite thin disc of thixkness dx with radius r = πr

^{2}r varies as y=√(x-1)

so volume of infinite thin disc = π(√(x-1))

^{2}dx = π (x-1)dxTotal volume = integrate this expression from x = 2 to x=5

total vulome = Π( x

^{2}/2 - x) with x varying from 2 to 5so total volume = Π ((5

^{2}/2 - 5) - (2^{2}/2 - 2)) = 7.5Π = 23.55 cubic units:)